Spreading speed for a diffusive foot-and-mouth disease model

Foot-and-mouth disease (FMD) is an acute, febrile, and highly contagious infectious disease caused by the foot-and-mouth disease virus. In this paper, we investigate the spreading speed of a reaction–diffusion system that models the spatial spread of foot-and-mouth disease. Since the system is nonmonotone, the comparison principle cannot be directly applied. To overcome this difficulty, we derive the outer spreading property by utilizing the fundamental structure of the model and employing a comparison method through a monotone upper-control system. Additionally, the inner spreading property is established using the comparison method via an interval-monotone lower-control system, along with a delicate analysis involving the fundamental solution of the Laplace operator. Our results provide an estimate of how rapidly the disease spreads. Finally, we conduct numerical simulations to examine the effects of diffusion rates for infectious individuals and viruses, as well as the infection rates on the spreading speed. Some sensitivity analyses of the spreading speed with respect to the model parameters are performed to determine the relative importance of these parameters in disease transmission.